What the internet says a fangirl is

Wikipedia has an entry for fan. It has a separate entry for fanboy. It does not have an entry for fangirl--a search will redirect you to fanboy. According to their discussion under "fan"

Fangirls tend to be more devoted to emotional and romantic aspects of their fandom, especially shipping...Fangirls of all persuasions are believed to be the largest contributors to fanfiction websites, sometimes disregarding the canon storyline of their fandom or altering it to fit either their own favored romantic pairings; or themselves into the continuity (termed self-insertions or Mary Sues).

while the "fanboy" entry says that

Stereotypical fanboys are attributed with a sycophantic devotion to the creators and principles behind a work with which they are currently enthralled. Fanboys are noted for a very emotional attachment to their chosen subject, often taking negative remarks about it as a personal attack. They will readily engage in debates, but will fall back on emotional responses when challenged on facts...

The term fangirl, while similar, often carries slightly different connotations. The term fangirl is often applied to any enthusiastic female fan, regardless of obsessive qualities or not, and is often used with overtones of "teenybopper".

Then I looked at the Merriam-Webster Open Dictionary and found this:

Fangirl/boy (noun) : A girl/boy that has an obsession [not fatal attraction-like] with a person, place, or thing, sometimes stemming from a TV series. movie, or manga/anime. Symptoms of fangirl/boyism are excessive drooling, squealing, and fan fictions that include the fangirl/fanboy and that person, place, or thing romantically involved. Can also be used as a verb.

n. Alex and Erin are complete fangirls for Kakashi from the manga series "Naruto". v. Cori, stop fanboying over Hinata!

This entry gives pretty much the same definition for both fanboy and fangirl, which makes it unique as far as I can tell, particularly since the combined definition includes characteristics that elsewhere are assigned only to "fangirl." That's linguistically unusual, applying the "feminine" characteristics to the broader category, but may have to do with the specific fandom referenced?

Urban Dictionary includes a whole list of competing definitions for "fangirl," some less complimentary than others.

My impression is that while there seems to be a fairly standard definition for "fanboy," the term "fangirl" is used far more broadly and possibly more situationally. I've most often seen it used as a slightly humorous synonym for "female fan," but that may have more to do with the parts of the net I frequent than with anything else, or with the specific realms of fandom I have an interest in. For example, a lot of the "extreme fangirl" examples I've seen referenced online have had to do with fans of anime or manga, neither of which I follow at all.

I do notice that female fans seem to be more open to using the term "fangirl" to refer to themselves, but I don't think that has to do with the term being less potentially derogatory, just less strictly defined and maybe more open to reclamation.